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1 results

  • Functional laws for trimmed Lévy processes

  • Part of
  • Boris Buchmann, Yuguang F. Ipsen, Ross Maller
  • Journal:
    Journal of Applied Probability / Volume 54 / Issue 3 / September 2017
    Published online by Cambridge University Press:
    15 September 2017, pp. 873-889
    Print publication:
    September 2017

  • Two different ways of trimming the sample path of a stochastic process in 𝔻[0, 1]: global ('trim as you go') trimming and record time ('lookback') trimming are analysed to find conditions for the corresponding operators to be continuous with respect to the (strong) J1-topology. A key condition is that there should be no ties among the largest ordered jumps of the limit process. As an application of the theory, via the continuous mapping theorem, we prove limit theorems for trimmed Lévy processes, using the functional convergence of the underlying process to a stable process. The results are applied to a reinsurance ruin time problem.